Realization of planar frequency selective fabrics and analysis of transmission characteristics

Abstract

Based on traditional frequency selective surfaces (FSSs), the research ideas of novel frequency selective fabrics (FSFs) are proposed. In this paper, the specific square-loop patch FSF was chosen as an example to illustrate the design procedures, including ANSYS (HFSS) simulation and numerical calculation methods, and then a computer-based experiment was conducted to develop prototypes. Although the simulation, calculation, and experiment results have minor differences, especially the resonance frequency, they show good consistency overall, which demonstrates that traditional design methods could also apply to 2D FSFs. The experiment transmission curve shows obvious band-stop response, peaking at -37.12 dB at the resonance frequency 11.65 GHz, and the narrow bandwidth of -10 dB is predicted from 10.85 GHz to 12.55 GHz. To further verify the validity of design procedures, two complementary cross-shaped FSFs were fabricated through a computer embroidery process, and the experimental transmission curves are complementary as expected, peaking at -26.05 dB and 0 dB at the same resonance frequency 9.65 GHz, and the narrow bandwidths of -10 dB and -0.5 dB are 1.07 GHz and 0.41 GHz, respectively. Although many problems need to be solved in further research, this convenient fabrication method and theoretical basis could make relevant work feasible in later study.

Keywords

electromagnetic functional fabric frequency selective surface equivalent circuit computer-based carving computer embroidery

Introduction

Electromagnetic (EM) wave shielding or absorption materials have been studied for many years,^1–3 including the soft fabrics,^4,5 which act as the last defence against the harmful EM environment. Traditionally, EM shielding fabrics are fabricated through a conductive polymer coating on the surface of existing fabrics,^6,7 or through conductive yarn weaving,^8,9 making the entire products continuously conductive and analogous to compact plates. However, the advantages of textiles in use depend on their properties of light weight, softness, and flexibility, especially for textile garments. However, the improvement of shielding effectiveness (SE) by increasing conductor mass conflicts with maintaining the comfort attributes of textiles, and it therefore becomes challenging to develop novel shielding fabrics with good SE as well as wearability properties.

In reality, general EM shielding fabrics are not as flat as expected, and many small holes exist due to the yarn weaving and buckling, but the EM leakage is subtle because of the coupling effect between adjacent conductors.¹⁰ The phenomenon indicates that holes of specific sizes and arrangement may not significantly affect SE, which could provide a new research direction. Study of the influence of periodic holes is necessary and meaningful, for the fabrics are periodic in structure. A frequency selective surface (FSS) is a kind of typical periodic structure, with non-continuous conductive units, which could selectively shield against EM waves, according to the frequency.^11,12 Therefore, it is possible to make novel EM wave shielding fabrics based on FSS theory and fabrication methods of textiles.

The effects of FSSs with different kinds of structure parameters are not singular, for they can show band-stop, band-pass, high-stop, or high-pass properties, and even double or multiple frequency-response characteristics.^13–15 Thus, the limit of the pure EM shielding effect could be surpassed, and the scope of application of EM functional textiles can be broadened if various frequency selective fabrics (FSFs) are developed. As one of the media in the EM field, FSFs can act as a spatial filter, which may be used in certain military and civil fields, regulating the transmission of EM waves effectively. People used to adopt printed circuit board (PCB) technology or photo-etching, digital carved milling, or laser machining and cutting to form the expected periodic pattern, and the obtained FSSs are mainly rigid plates and composites,¹⁶ which are widely used in various applications of airborne radomes, sub-reflectors, terahertz sensing, circuit analogue absorbers, etc.^14,17 Compared with the traditional rigid plates, novel FSFs certainly have unique advantages, and may be applied to light absorbing materials, e-textile antenna, frequency selective communication windows, etc.¹⁸ This paper proposed research ideas of FSFs, including the design procedures and fabrication methods, and further discusses the potential difficulties and feasibility in later study.

Design procedures

HFSS simulation

The proposed FSFs in this paper were composed of two layers: the upper FSS layer and the lower flexible fabrics. The square-loop patch FSF was taken as an example to demonstrate the design process, which can also be applied to other kinds of FSFs. For the convenience of modelling, the fabric was assumed to be a smooth plate with constant thickness and EM properties, and the conductive patch was assumed to be a perfect conductor, with a thickness of 0.04 mm.

Using Floquet’s theorem for periodic surfaces, a unit cell geometry model was built in HFSS, as shown in Figure 1(a), in which Master–Slave boundary conditions and Floquet port were utilized to simulate the infinite periodic structure and the excitation of the EM wave. Figure 1(b, c) shows the top and side view of the unit cell model, respectively, in which Dx and Dy are the lateral and longitudinal dimensions of the unit cell, m and n are the side lengths of the outer and inner square, and t is the equivalent thickness of the base fabric.

Figure 1.

(a) Unit cell geometry model of FSF in HFSS. (b) Top view of the unit cell model. (c) Side view of the unit cell model.

The influence rules of structural as well as physical parameters can be obtained by simulating analysis, and the optimum structure with expected transmission characteristics can be confirmed by an optimization process. Figure 2(a),(b) shows the transmission curves of several assumed FSFs, from which we can see the influences of geometric parameter, n, and physical parameter, ɛ_r, respectively. The influence of other parameters are not discussed here, considering the similarity in analysis methods.

Figure 2.

(a) Influence rule of geometric parameter n (Dx = Dy = 18 mm, m = 10 mm, ɛ_r = 1). (b) Influence rule of physical parameter ɛ_r (Dx = Dy = 18 mm, m = 10 mm, n = 6 mm).

As the value of n or ɛ_r increases gradually, the transmission curves move towards lower positions, while the corresponding bandwidths show invisible changes, as shown in Figure 2(a),(b), respectively. All the simulated resonance frequencies (f_{0_S}) are listed in Tables 1 and 2 for comparison.

Table 1.

Calcaulated L, C, and f_{0_C} values of the assumed FSFs in Figure 2(a)

n (mm)	L(nH)	C(fF)	f_{0_C} (GHz)	f_{0_S} (GHz)
4	2.62	43.84	14.86	14.72
5	2.99	41.01	14.36	14.02
6	3.39	38.66	13.89	13.04
7	3.86	36.50	13.34	12.49
8	4.53	34.58	12.72	11.88

Table 2.

Calcaulated L, C, and f_{0_C} values of the assumed FSFs in Figure 2(b)

ɛ_r	L(nH)	C(fF)	f_{0_C} (GHz)	f_{0_S} (GHz)
1	3.39	38.66	13.89	13.04
3	2.79	64.85	11.81	11.14
5	2.58	90.24	10.42	9.95
7	2.48	115.34	9.41	8.93
9	2.41	140.38	8.65	8.25

Numerical calculation by EC model

To further investigate the filtering mechanism and quantitatively calculate the resonance frequency, the classical equivalent circuit model was adopted. When the incident wave is polarized either parallell or perpendicular to the strip gratings, the shunt impedance is inductive or capacitive, as shown in Figure 3(a, b), respectively. The square-loop patch element is composed of two kinds of orthogonal strips and therefore the L-C series circuit can be derived to characterize the compound effect, as depicted in Figure 3(c).^19–21

Figure 3.

(a) Equivalent circuit of inductive strip gratings. (b) Equivalent circuit of capacitive strip gratings. (c) Equivalent circuit of square-loop patch FSF.

For normal incidence of EM waves, the inductive reactance (X_L) and capacitive susceptance (B_C) can be calculated from formulae (1) and (2), where Z₀ is the characteristic impedance of free space (=377 Ω) and Y₀ is the admittance (=1/Z₀), f and λ are the frequency and wavelength of operating EM waves, β_L and β_C are functions of the width of metal strip (m–n) and the interval spacing between two units (D–m), which can be calculated from formulae (3) and (4), respectively, ɛ_c is a correction factor to adjust the effect of the substrate, which is derived from formula (5), and G is a compensation factor given by formula (6)

\frac{X_{L}}{Z_{0}} = \frac{2 π fL}{Z_{0}} = \frac{m}{λ} [- \ln β_{L} + G_{L}]

(1)

\frac{B_{C}}{Y_{0}} = \frac{2 π fC}{Y_{0}} = \frac{4 m}{λ} [- \ln β_{C} + G_{C}] ɛ_{c}

(2)

β_{L} = \sin \frac{π (m - n)}{2 D}

(3)

β_{C} = \sin \frac{π (D - m)}{2 D}

(4)

ɛ_{c} = \frac{ɛ_{r} + 1}{2}

(5)

G_{W} = \frac{1}{2} \frac{(1 - β_{W}^{2}) 2 [2 A (1 - \frac{β_{W}^{2}}{4}) + 4 A 2 β_{W}^{2}]}{(1 - \frac{β_{W}^{2}}{4}) + 2 A β_{W}^{2} (1 + \frac{β_{W}^{2}}{2} - \frac{β_{W}^{4}}{8}) + 2 A 2 β_{W}^{6}}

(6)

where, G_W can be G_L or G_C and β_W is the corresponding β_L or β_C, A can be obtained from formula (7), and the characteristic impedance of FSF (Z) can be derived from formula (8)²²

A = \frac{1}{\sqrt{1 - (\frac{D}{λ}) 2}} - 1

(7)

Z = j (2 π fL - \frac{1}{2 π fC})

(8)

As the value of Z approaches zero, a resonance phenomena will appear, and the resonance frequency can be derived from formulae (1)–(8). For FSFs which do not lose EM energy, the reflectivity (R) and transmission coefficient (S₂₁) can be further calculated on the basis of transmission line theory and lumped parameters, according to formulae (9) and (10), separately, and the relationship between the transmission coefficient and the frequency (S₂₁–f) curves can be established^23,24

R = | - \frac{Z_{0}}{2 Z + Z_{0}} |

(9)

S_{21} = 10 \lg (1 - R)

(10)

To comparatively analyze the simulated and calculated results, the corresponding L, C, and f_{0_C} of the assumed FSFs in Figure 2 were calculated, and are listed in Tables 1 and 2, together with f_{0_S}. The calculated transmission curve of a specific FSF is shown in Figure 4 for comparison.

Figure 4.

Experiment, simulation, and calculation results of square-loop patch FSF.

In Table 1, when the value of n increases from 4 mm to 8 mm, L increases from 2.62 nH to 4.53 nH while C decreases gradually from 43.84 fF to 34.58 fF. The variation amplitude of L is larger, which causes f_{0_C} to move to lower positions (from 14.86 GHz to 12.72 GHz). In Table 2, when the value of ɛ_r increases from 1 to 9, L decreases slightly from 3.39 nH to 2.41 nH while C increases from 38.66 fF to 140.38 fF gradually. Then the effect of C is larger, causing f_{0_C} to move to lower positions (from 13.89 GHz to 8.65 GHz) as well. From the last two columns, it can be seen that f_{0_C} is slightly larger than f_{0_S} on the whole, which can be mainly attributed to the coupling effect between inductive and capacitive strips, which was not considered in the calculation.

Alhough f_{0_S} and f_{0_C} are not completely identical, they show similar variation rules, and the gaps between them are within the acceptable range. By means of the two methods, the planar FSFs with expected transmission characteristics can be designed effectively and the methods can also provide a theoretical basis for relevant analysis and characterization.

Experiment

Fabrication and test of square-loop patch FSF

To verify the validity of the design procedures, a square-loop patch FSF with specific parameters (Dx = Dy = 18 mm, m = 10 mm, n = 6 mm) was fabricated using a computer-based carving experiment, and the transmission characteristics were tested using the Shielding Room Method. The relevant fabrication process and test principles were illustrated at length in the previous work.^25,26 Plain polyester fabric was selected as the substrate: the count of warp and weft yarn was 16.8 tex, the density of arrangement was 408 × 274 in 10 cm, the weight of the fabric was 124 g/m², and the equivalent thickness was 0.2 mm. The dielectric coefficient value of the polyester fabric was tested to be near 1.0 using the Parallel Plate Method, when the frequency was set at 1 GHz. The thickness of conductive layer was deterimined to be 0.04 mm, consistent with the simulation assumption.

Analysis of transmission characteristics

The experiment, simulation, and calculation results are given in Figure 4, which shows that the three curves have an analogous trend in the given frequency band, overall. However, there are some differences in the resonance frequencies (f_{0_E}, f_{0_S}, and f_{0_C}) and peaks, which can be attributed to the processing precision, the finiteness of the sample size, the imperfection of the conductive metal, the uneveness of fabric surface due to yarn buckling, and many other factors, which were not considered in the simulation and the calculation. Although the experiment transimission curve is not as ideal as expected, it shows obvious band-stop response, peaking at -37.12 dB at the resonance frequency 11.65 GHz. The bandwidth of -10 dB (more than 90% of EM waves can be shielded) is predicted from 10.85 GHz (point A) to 12.55 GHz (point B) in the figure, which is very narrow and can meet certain requirements during use.

Realization of other FSFs

To explore the applicability of other kinds of FSFs, as well as the validity of various fabrication methods, the simulation method was used to design two complementary cross-shaped FSFs aiming at 10 GHz, and a computer embroidery experiment was conducted to prepare the prototypes with optimum structures. A computer-based JANPME MB-4 embroidery machine with embroidery area up to 240 × 200 mm and a conductive embroidery thread (70/30 polyster/stainless steel wire, 40 S/3) with the resistivity of approximately 2 × 10⁻⁴ Ω·m were used to fabricate the FSFs. The polyester fabric in the above computer-based carving experiment was also selected here as the substrate. The type of needle tracking was organization filling, with a 45° inclined stitch, and the stitch spacing and length were set as 0.8 mm and 4.2 mm, respectively. The embroidery speed was controlled at 600 spm, considering the strength and tension of the conductive thread. The machining process for computer embroidery and photographs of the fabricated patch FSF and aperture FSF are shown in Figure 5.

Figure 5.

(a) Machining process of computer embroidery. (b) Photograph of cross-shaped patch FSF. (c) Photograph of cross-shaped aperture FSF.

The experiment and simulation results of the proposed complementary cross-shaped FSFs are given in Figure 6, from which it can be seen that the two experiment curves of fabricated FSFs coincide with the corresponding simulation curves, especially the patch FSF, which further verifies the effectiveness of the design process. The reason for the small deviation can be attributed to the fabrication process and imperfect materials, similar to the above square-loop patch FSF.

Figure 6.

Experiment and simulation results of two complementary cross-shaped FSFs.

The two experiment curves show typical band-stop and band-pass characteristics, which are complementary within the given frequency range, with the same resonance frequency, 9.65 GHz. For the transmission curve of patch FSF, the peak comes to -26.05 dB (nearly all the incident waves can be shielded), and the bandwidth of -10 dB is approximately 1.07 GHz, from 9.25 GHz (point C) to 10.32 GHz (point D) in the figure, for incident plane waves. For the transmission curve of aperture FSF, the peak reaches almost 0 dB (corresponding EM wave could pass through the FSF totally), and the bandwidth of -0.5 dB (approximately more than 90% of EM waves can traverse the FSF) is even narrower, predicted from 9.67 GHz (point E) to 10.08 GHz (point F).

Difficulty and feasibility

The two kinds of FSFs proposed above are both 2D. Actually, FSF products are far more complex, for the unit shape can be various and multi-level, and even 3D FSFs can be designed based on established theory. More efforts should be devoted to overcoming the following difficulties.

First, as a kind of soft material, textiles are flexible, which makes the frequency–response characteristics of FSFs susceptible to fluctuation. Besides, the size of the conductive units may be imprecise due to the surface roughness and softness of textiles, causing a deviation in expected results. Also, the fitering mechanism of novel FSFs should be further studied, considering the complex space configuration of textiles, such as spacer fabrics, velvet, and plush fabrics, etc.

Relevant research is still feasible, although many problems still need to be solved. The wavelength of microwaves and the fineness of fibers are of the same order of magnitude, which makes relevant research much easier. Also, the fabrication methods of FSFs are not limited to computer-based carving and computer embroidery processes: other methods, such as silk-screen or inkjet printing, cloth hot stamping, regional electro- or electroless plating, local magnetron sputtering, and different fabrication technologies for textiles (weaving, knitting, or braiding), etc., can be used to prepare FSFs. More conductive materials, no matter what the form is, can be adopted to make the obtained FSFs work.

Conclusions

A novel square-loop patch FSF was taken as an example to illustrate the design process, and the fabricated FSF shows obvious band-stop response with ideal bandwidth and resonance peaks, which indicates that traditional simulation as well as numerical calculation methods can also apply to 2D FSFs. To further study the applicability of the design procedures, specific cross-shaped patch and aperture FSFs were fabricated through a computer embroidery process, and experiment and simulation results showed good consistency. The experiment transmission curves of patch and aperture FSFs are complementary, as expected, peaking at -26.05 dB and 0 dB at the same resonance frequency, 9.65 GHz, and the narrow bandwidths of -10 dB and -0.5 dB are at 1.07 GHz and 0.41 GHz respectively. Related research is feasible and more work should be devoted to the many problems that still need to be solved.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors acknowledge support from the Fundamental Research Funds for the Central Universities (grant number CUSF-DH-D-2015005).

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